The present disclosure relates generally to methods and apparatuses for measuring changes in length or position; more particularly it relates to reducing the data age differences or position uncertainty between the multiple measurements of length or position.
The use of interferometry to measure changes in position, length, distance or optical length is well known, see for example “Recent advances in displacement measuring interferometry” N. Bobroff, Measurement Science & Technology, pp. 907-926, Vol. 4, No. 9, September, 1993 and U.S. Pat. No. 4,688,940 issued Aug. 25, 1987. A typical displacement measuring interferometer system consists of a frequency-stabilized light source, interferometer optics and measuring electronics. The interferometer optics split the laser light into a reference path and a measurement path, then recombine the light returning from the two paths and direct the recombined light to a photodiode where it produces an interference signal. A distance change of one wavelength in the measurement path relative to the reference path produces a phase change of 360 degrees in the interference signal. The measuring electronics measure and accumulate the change in phase and provide a position output for the application.
In many applications, heterodyne interferometry, in which the measurement and reference beams differ in frequency, is preferred. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optic modulation, or internal to the laser using birefringent elements or the like. The measurement and reference beams may be orthogonally polarized, allowing a polarizing beam splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/λ, where v is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2π phase change corresponding to a distance change L of λ/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
Heterodyne interferometers may also be of the dispersion type. In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm, and are used to measure the dispersion of a gas in the measurement path of a distance measuring interferometer. The dispersion measurement can be used to convert the optical path length measured by a distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged. In addition to the extrinsic dispersion measurement, the conversion of the optical path length to a physical length requires knowledge of an intrinsic value of the gas. The factor Γ is a suitable intrinsic value and is the reciprocal dispersive power of the gas for the wavelengths used in dispersion interferometry. The factor Γ can be measured separately or taken from published literature values.
Many interferometer applications, such as step-and-scan photolithography tools used to manufacture integrated circuits, require measuring multiple axes of motion at high velocity and with high resolution. An advanced photolithography system may include measurement of, for example, eight or more axes. The accuracy requirements increase as the size of the features on the measured object decrease. Rapidly increasing accuracy demands and needs for determining the precise timing of multiple dynamic interferometric position measurements at higher accuracy have fueled numerous efforts to reduce and minimize the various sources of uncertainty that are inherent in currently known methods and apparatus.
To achieve full accuracy with dynamic multi-axis measurements, all measurements should have the same data age, such that simultaneous measurement of each axis represents the same instant in time. Data age is defined as the time from when a change in interferometric position occurs to when the data representing the measured position is output. In a multi-axis dynamic system, when the system relies on position values from several different axes in motion, small differences in data age between axes can result in significant measurement errors. Similarly, small shifts in the phase of the measurement signal can result in significant measurement errors.
Two forms of inherent uncertainty are called fixed delay and variable delay. Fixed delay arises from differences in cable lengths, optical path lengths, photoelectric detector delay, and phase meter offsets in interferometry systems, whereas circuit delay, i.e., group delay, (which varies with signal frequency) gives rise to variable delay. The effects of these delays create differences in the data age of the interferometrically measured values, i.e., the elapsed time between the event representing the position measurement, and when the position data is available to the user. Compensating the data age by adjusting one or more of the delays is generally impractical.